Effective Hard-sphere Diameter Research Articles

A comparative study on surface tension, diffusion coefficient and shear viscosity coefficient of liquid transition metals

Surface tensions of liquid transition metals of the 3d, 4d and 5d series have been calculated using modified Mayer’s formula involving hard sphere (HS) interaction of liquids derived from first and second order approximations of Percus–Yevick (PY) solutions of isothermal compressibility. Effective HS diameter and packing fraction are key ingredients of this study. To determine them, we have used effective pair potential derived from both Bretonnet–Silbert (BS) pseudopotential model and many body potential obtained from embedded atom method (EAM) in conjunction with variational modified hypernetted chain (VMHNC) integral equation theory of liquid structure. Calculated values of surface tension are used to evaluate transport coefficients such as diffusion and shear viscosity coefficients. Comparing with experimental and simulated data, calculated results suggest that expression derived from second order approximation of PY solution with the combination of EAM potential and VMHNC theory works better than any other combinations for the concerned systems.

Integral equation theories for fluid with very short-range screened Coulomb plus power series interactions

Monte Carlo NVT simulations have been performed to obtain the thermodynamic and structural properties of fluids with a potential consisting in a hard-core and screened Coulomb plus power series (HC-SPS) interactions for three sets of the potential parameters. These ‘exact’ data are used to check the accuracy of two integral equation theories and a local excess chemical potential formula for very short-ranged potentials. The theories considered are the reference hypernetted-chain (RHNC) approximation and the local self-consistent OZ approximation (LSCOZA). The main conclusions of our study are described below. (i) The RHNC always underestimates the first peak of the radial distribution, which directly leads to an underestimation of the pressure and an overestimation of excess internal energy. In general, as the potential range becomes shorter ranged and the temperature decreases, the performance of the RHNC worsens and even becomes qualitatively incorrect. (ii) Local pressure self-consistency is of crucial importance to ensure that the hard sphere bridge function with an effective hard sphere diameter yields very accurate results for the pressure and excess internal energy even for very short-range potentials and at temperatures very close to the critical temperature. (iii) The accuracy of the excess chemical potential, obtained by thermodynamic integration of the excess internal energy, is also remarkable even for very short-ranged potentials and superior to that of a local excess chemical potential formula previously proposed [S. Zhou, Theor. Chem. Acc. 117, 555(2007)].

Analytical treatment of the structure for systems interacting via core-softened potentials

We consider a double ramp (DR) model of the family of core-softened potentials which possess a liquid–liquid critical point when the energy parameter h is negative, as in the Jagla potential [E. A. Jagla, Phys. Rev. E 63, 061501–5 (2001)]. Our model offers the possibility of gradually passing from an attractive potential to a purely repulsive potential by varying the energy parameter h. Using a mean field density functional theory and the MC simulation, we determine the structure factor of the DR model for different values of the parameters. We show that the DR model belongs to the class of adaptable potentials continuously evolving between waterlike and hard sphere (HS) systems. The HS structure factor necessary for the analytical treatment is defined in terms of the effective HS diameter σe which is a function of temperature and density, and which makes it possible to predict the structure as a function of temperature with fairly good precision.

On the choice of the effective diameter in the high-temperature expansion for the Lennard–Jones fluid

A third-order perturbation theory, within the framework of the high temperature expansion, with the perturbation terms obtained from computer simulation, is used to test the performance of several prescriptions proposed in the literature to obtain the effective hard-sphere diameter for the Lennard–Jones fluid. It is found that the classical Barker–Henderson prescription provides, on the whole, the best accuracy as compared with the available simulation data for the excess energy, the equation of state and the liquid-vapour coexistence densities.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a ‘soft colloids make strong glass-forming liquid’-type of behavior observed close to the nominal glass transition volume fraction, φg. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φg. Above φg, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

Verification of the Stokes-Einstein relation in liquid noble metals over a wide range of temperatures

The validity of Stokes-Einstein (SE) relations in liquid noble metals namely Cu, Ag and Au over a wide temperature range has been studied using Dzugutov's scaling scheme and Faber's hard-sphere (HS) theory of transport coefficients. Basic ingredients of those theories are the temperature-dependent effective HS diameter and excess entropy. To determine them, we have applied variational modified hypernetted chain theory in conjunction with effective interionic interaction derived from embedded atomic method (EAM) with both temperature-dependent and independent adjustable parameters α and b. Obtained ingredients using α(T) and b(T) are close to the available experimental data than those obtained using fixed α and b with an empirical relation. Calculated transport coefficients are in good agreement with experimental data when scaling scheme with α(T) and b(T) has been considered. Simplified SE relations from transport coefficients hold when scaling scheme has been applied with α(T) and b(T) and lies around the slip boundary line.

Effects of interionic pair interactions on atomic transport properties of liquid Al

The effects of parameters used for tuning the interionic pair interaction of the Ashcroft’s pseudopotential model on the temperature-dependent atomic transport properties of liquid Al have been studied employing the Universal Scaling Laws (USLs) and Hard Sphere (HS) theories of liquid metals. Temperature-dependent effective HS diameter and excess entropy are the key ingredients of the applied theories. We have calculated them by using Ashcroft’s empty core (EMC) pseudopotential and the variational modified hypernetted chain (VMHNC) integral equation theory of liquid. Obtained results clearly suggest that the core radius in the interaction plays a major role in determining atomic transport properties of liquid Al for both USLs and HS theory. It is also observed that USLs are more sensitive than HS theories in response to variation of core radius.

Validity of the Stokes−Einstein relation in liquid 3d transition metals for a wide range of temperatures

The validity of Stokes−Einstein (SE) relations obtained from both slip and stick boundary conditions has been investigated for an extending temperature range approximately 250 K from the melting points of liquid Fe, Co and Ni using Dzugutov scaling scheme for transport coefficients. The basic ingredients of Dzugutov scaling scheme are the temperature dependent effective hard-sphere (HS) diameter, σ(T), and the excess entropy, Sex(T). Sex is calculated considering both two (S2) and many body approximations (ST) of liquid atoms. For both ingredients, we have applied variational modified hypernetted chain (VMHNC) integral equation theory in conjunction with both Brettonet−Silbert (BS) pseudopotential and many body potential obtained from embedded atom method (EAM). Calculated transport coefficients using the combination of EAM and ST are in better agreement with available literature values than any other applied combinations. We observe that SE relation holds for the studied representative systems when the combination of EAM potential and ST has been considered.

A comparative study on atomic transport properties of liquid less-simple metals

We have studied the atomic transport properties of liquid less-simple metals namely Bi, Cd, Pb, Sb, Sn and Tl using universal scaling laws and hard sphere (HS) theories of liquid. Effective interionic interaction in metals has been derived from both Brettonet–Silbert (BS) and Ashcroft’s empty core pseudopotential models. For structure calculation, variational modified hypernetted chain integral equation theory has been considered. Excess entropy and effective HS diameter are the basic ingredients of the study. Obtained ingredients are found to be close with experimental data than any other available literature values when BS model has been chosen. Comparing with experimental data, obtained results for transport coefficients suggest that Faber’s HS theory is excellent for diffusion coefficient and is reasonably good for viscosity coefficient along with BS pseudopotential than any other combinations employed in this study. The probable reason may be the hybridization of s and d electrons exists in the concerned systems.

Assessment of scaled particle theory predictions of the convergence of solvation entropies

Entropy convergence is the experimental observation that the hydration entropies of families of non-polar solutes cross one another and converge at a distinct temperature above the boiling point of water. Entropy convergence has subsequently received significant theoretical and molecular simulation interest to interpret its molecular origin. Classic scaled particle theory has enjoyed success in describing entropy convergence for cavity-like, hard sphere solutes in water despite the fact it only considers water's equation-of-state and effective hard sphere diameter while neglecting liquid state inter-molecular correlations. This stands in difference to traditional interpretations of the hydrophobic effect that invoke water's three-dimensional structure when describing aqueous solutions of non-polar moieties. Here we investigate the origins of entropy convergence in classic scaled particle theory. We demonstrate convergence results from the theory's unphysical prediction that the surface tension of the solvent against a hard, flat interface exhibits a maximum as a function of temperature, indicative of a surface entropy that changes sign from negative to positive values with increasing temperature. In addition, we find that classic scaled particle theory can predict convergence like behavior in an organic liquid for which the phenomenon is unexpected.

An equation of state for Stockmayer fluids based on a perturbation theory for dipolar hard spheres.

We develop a perturbation theory for the difference between the Helmholtz energy of a Stockmayer fluid, i.e., a fluid interacting by a Lennard-Jones plus point-dipole potential, and a Lennard-Jones fluid. We show that the difference can be approximated by the perturbational Helmholtz energy contribution of a dipolar hard-sphere fluid with a suitably chosen effective hard-sphere diameter, relative to a hard-sphere fluid with the same effective diameter. We analyze both a third and fourth order perturbation theory, both written as Padé approximations. Several recipes for calculating the hard-sphere diameter are investigated; we find that the Weeks-Chandler-Andersen diameter is most suitable. Results of the perturbation theory are shown to be in good agreement with reference data for the Helmholtz energy, internal energy, and isochoric heat capacity as obtained from molecular simulations performed in this work and to vapor-liquid equilibrium data from the literature. Theoretical predictions of the proposed model are compared to results from the perturbation theory of Gubbins and Twu [Chem. Eng. Sci. 33, 863 (1978)], which is a theory based on a Lennard-Jones reference fluid. We find the theories are in good agreement. Our approach can easily be applied to van der Waals potentials, other than Lennard-Jones potentials. If a dipolar Mie fluid is considered, the approach merely requires calculation of the effective hard-sphere diameter for a Mie potential. We further note that the approach has a reduction in the variable space of the underlying correlation integrals, i.e., the correlation functions of a hard-sphere fluid depend on density only, whereas the Lennard-Jones reference correlation functions depend on density and temperature.

Study of Energy of Formation for FexNi1-x Liquid Binary Alloys

In this present study we have systematically calculated the free energy of formation for FexNi1-x binary alloys at a thermodynamic state T = 1920 K. A microscopic theory bases on first order perturbation theory along with a reference hard sphere liquid has been applied. The interionic interaction is described by Bretonnet-Silbert local pseudopotential that capable of takes into account the s-d hybridization in electro-ion interaction in transition metals. The effective hard sphere diameters have been determined using linearized Weeks-Chandler-Andersen (LWCA) perturbation theory and the partial structure calculated in line with Ashcroft and Langreths original work. The calculated theoretical value and available experimental data for free energy of formation are in agreement quite satisfactorily.

On the ability of classic scaled particle theory to reproduce the cavity contact correlation function of water over a large hydrostatic pressure range

The cavity contact correlation function G(RC) represents the density of liquid molecules in contact with the surface of a spherical cavity of RC radius normalized to the bulk density. Recently, the G(RC) function of water has been determined in the TIP4P water model at 25 °C and over a large range of hydrostatic pressure, by means of Monte Carlo simulations [Floris, J. Mol. Liq. 218 (2016) 166]. It is shown that classic scaled particle theory relationships are able to reproduce in a satisfactory way the hydrostatic pressure dependence of G(RC) by using only two input data: the experimental density of water, and the effective hard sphere diameter of water molecules, 2.8 Å, assumed to be pressure-independent. No further information is needed, even though G(RC) should reflect structural features of water.

Measurement and modeling of the viscosity of (nitrogen + carbon dioxide) mixtures at temperatures from (253.15 to 473.15) K with pressures up to 2 MPa

Abstract The viscosity of pure nitrogen and of three (nitrogen + carbon dioxide) mixtures was measured over the temperature range from (253.15 to 473.15) K with pressures up to 2 MPa utilizing a rotating-body viscometer. The relative combined expanded uncertainty (k = 2) in viscosity was estimated to be between (0.14 and 0.19)% for nitrogen. For the binary gas mixtures, the uncertainty ranged between (0.19 and 0.39)%. The new data for nitrogen show very good agreement with experimental data from the literature and with recent ab initio calculations. The experimental data for the binary mixtures were compared with an Extended Corresponding States (ECS) model as implemented in the NIST REFPROP 9.1 database. The relative deviations of the data from the model were generally found to increase in magnitude with increasing density and ranged between (−2.1 and 0.4)% near the greatest density studied. The experimental data were correlated using the modified Enskog theory for hard sphere mixtures correct to the second viscosity virial coefficient. In this analysis, the effective hard-sphere diameters determining (a) the zero-density viscosity and (b) the leading term in the radial distribution function at contact were correlated as functions of temperature. The resulting model was found to represent all measured data with absolute relative deviations

Thermodynamic properties of fluids with Lennard–Jones–Gauss potential from computer simulation and the coupling parameter series expansion

ABSTRACTMonte Carlo NpT simulations have been performed to obtain the pressure, excess enthalpy, excess internal energy, isothermal compressibility coefficient, thermal expansion coefficient and constant-pressure excess heat capacity of fluids with several kinds of Lennard–Jones–Gauss potential models from subcritical to supercritical and from vapour to liquid states. These data have been used to assess the performance of a perturbation theory, namely the coupling parameter series expansion (CPSE) of the Helmholtz free energy, for continuous potential models without hard-sphere core. The main findings are summarised as follows: (1) The analysis of the results for the constant-pressure excess heat capacity shows that the CPSE is convergent until seventh order. (2) The seventh-order CPSE, when combined with the simple Barker–Henderson (BH) effective hard-sphere diameter, predicts rather accurately the thermodynamic properties, except at high densities and low temperatures. (2) The loss of accuracy in these situations is attributed to the inadequacy of the BH prescription that does not account for the density dependence of the effective hard-sphere diameter. (3) The CPSE performance is rather insensitive to the details of the potential model considered.

Thermodynamic properties of diamond and wurtzite model fluids from computer simulation and thermodynamic perturbation theory

Monte Carlo NVT simulations have been performed to obtain the thermodynamic and structural properties and perturbation coefficients up to third order in the inverse temperature expansion of the Helmholtz free energy of fluids with potential models proposed in the literature for diamond and wurtzite lattices. These data are used to analyze performance of a coupling parameter series expansion (CPSE). The main findings are summarized as follows, (1) The CPSE provides accurate predictions of the first three coefficient in the inverse temperature expansion of Helmholtz free energy for the potential models considered and the thermodynamic properties of these fluids are predicted more accurately when the CPSE is truncated at second or third order. (2) The Barker–Henderson (BH) recipe is appropriate for determining the effective hard sphere diameter for strongly repulsive potential cores, but its performance worsens with increasing the softness of the potential core. (3) For some thermodynamic properties the first-order CPSE works better for the diamond potential, whose tail is dominated by repulsive interactions, than for the potential, whose tail is dominated by attractive interactions. However, the first-order CPSE provides unsatisfactory results for the excess internal energy and constant-volume excess heat capacity for the two potential models.

Thermophysical properties of ionic liquids and their mixtures from a new equation of state

In our previous work, a perturbed hard-trimer-sphere equation of state (PHTS EOS) was developed for modeling the phase equilibria of pure ionic liquids (ILs) (M.M. Alavianmehr et al., Ionics 22 (2016) 2447–2459). In this work, we have successfully extended the model to the mixtures of IL + IL and IL + solvent. Two temperature-dependent parameters appearing in the EOS are correlated with two microscopic scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The overall average absolute deviation (AAD) of the estimated densities from the literature data using the proposed model with and without non-additivity parameter (λij) was found to be 0.44 and 0.79%, respectively. A modified Enskog equation and rough hard-sphere (RHS) theory are combined with our proposed equation of state to calculate the viscosity coefficient of ionic liquids and their mixtures. Finally, from the results obtained, a linear relation between logarithm of surface tension and viscosity property of ionic liquid was developed.

Universal scaling of pair-excess entropy and diffusion in Yukawa liquids

Understanding diffusion in liquids from properties of static structure is a long standing problem in condensed matter theory. Here, we report an atomistic study of excess entropy and diffusion coefficient in a strongly coupled Yukawa liquid. We observe that the pair excess entropy s2 scales with temperature as −3.285 (Tm/T)0.665 and contributes to about 90% of the total excess entropy close to the freezing transition Tm. We further report that at low temperatures where the diffusive transport is mediated by cage relaxation, the diffusion coefficient when expressed in natural units of the Enskog collision frequency and the effective hard sphere diameter, obeys the scaling law 0.04 es2 and deviates from it at high enough temperatures where cages cannot form.

Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

We generalize our microscopic, force-level, self-consistent nonlinear Langevin equation theory of activated diffusion of a spherical particle in a dense hard sphere fluid to treat molecular penetrant diffusion in homopolymer melts and nonaging glasses. A coarse-grained mapping is developed where polymer chains are modeled as disconnected, noninterpenetrating Kuhn scale hard spheres (diameter, σ), and the penetrant is modeled as an effective hard sphere (diameter, d) which can be attracted to the polymer segment. The polymer mapping is a priori carried out by enforcing the effective hard sphere fluid reproduces the specific polymer liquid or glass long wavelength dimensionless collective density fluctuation amplitude. The theory predicts that penetrant diffusivity exhibits supra-Arrhenius temperature dependence in supercooled polymer melts and (near) Arrhenius temperature dependence in quenched nonequilibrium polymer glasses. Polymer–penetrant attraction slows down penetrant diffusivity to a degree that is...

Application of perturbed hard-sphere equation of state to the study of volumetric properties of nano-fluids

This paper aimed to examine the application of a perturbed hard-sphere (PHS) scheme for modeling the volumetric properties of nanofluids. In this regard, PHS scheme has been employed to develop an analytical equation of state (EOS) to correlate and predict the volumetric properties of some nanofluids containing SnO2,ZnO, Co3O4, TiO2-anatase (-A), TiO2-rutile (-R), CuO and Al2O3 as nanoparticles dispersed in ethylene glycol, poly ethylene glycol, water, poly ethylene glycol + water and ethylene glycol + water as base fluids. Two temperature-dependent parameters appeared in the EOS were expressed in terms of molecular scaling constants σ, the effective hard-sphere diameter, and ε, the non-bonded interaction energy. The aforementioned scaling constants were correlated with melting temperatures and true densities which demonstrated the rationality of these constants. The performance of the proposed model was assessed by predicting 1348 density data, for which their measured values were available in the literature over the pressure range from 0.1 to 45 MPa and temperature range from 273 to 363 K. The overall average absolute deviation (AAD) of the correlated (at 0.1 MPa) and predicted (at elevated pressures) densities of 9 studied nanofluids from the experimental data was found to be 0.44%. Generally, this work showed that PHS is an appropriate scheme for the correlation and prediction of the properties of this class of fluids by the help of crossed interaction parameters between nanoparticles and base fluid molecules. The isothermal compressibility coefficients and excess volumes of studied nanofluids have also been investigated by the proposed model.